Given equations that define a region in the plane students are asked to find its area, the volume of the solid formed when the region is revolved around a line, and/or the region is used as a base of a solid with regular cross-sections. This standard application of the integral has appeared every year since…

The long name is “Here’s the graph of the derivative, tell me things about the function.” Students are given either the equation of the derivative of a function or a graph identified as the derivative of a function but no equation is given. It is not expected that students will write the equation (although this…

We continue the discussion of the various type questions on the AP Calculus Exams with linear motion questions. “A particle (or car, or bicycle) moves on a number line ….” These questions may give the position equation, the velocity equation (most often), or the acceleration equation of something that is moving, along with an initial…

The Free-response Questions There are ten general categories of AP Calculus free-response questions. As I’ve done in part years, I will consider each individually over the next few weeks posting on Tuesdays and Fridays. These will be updates of last year’s posts. Here is the list of the types and the schedule: Tuesday March 6 –…

This is a list of links to some resources for reviewing. How, Not Only to Survive, but to Prevail… – Notes and advice for your students. You may copy and duplicate this for your class. Calculator Use on the AP Exams – hints and instruction. Ted Gott’s Free-response Index – an excel spreadsheet searchable by…

It will soon be time to start reviewing for the AP Calculus Exams. So, it’s time to start planning your review. For the next weeks through the beginning of April I will be posting notes for reviewing. There are not new; versions have been posted for the last few years and these are only slightly…

Good Question 14 – The Integral Test I have no criteria for what constitutes a “Good Question” for this series of occasional posts. They are just questions that I found interesting, or that seem more than usually instructive, or that I learn something from. I cannot quote this question (2016 BC 92) since it is…

Ideally, as with parametric and vector functions, polar curves should be introduced and covered thoroughly in a pre-calculus course. Questions on the BC exams have been concerned with calculus ideas related to polar curves. Students have not been asked to know the names of the various curves (rose, curves, limaçons, etc.). The graphs are usually…

In last’s Friday’s post I really didn’t answer this question. Rather, I tried to show that there is not only one convergence test that must be used on a given series. Nevertheless, the form of a series suggest a test that is likely to work. In this post, I’ll try to give some suggestions as…

n the plane, the position of a moving object as a function of time, t, can be specified by a pair of parametric equations or the equivalent vector . The path is the curve traced by the parametric equations or the tips of the position vector. . The velocity of the movement in the x- and y-direction is given by the vector . The vector…

One common question from students first learning about series is how to know which convergence test to use with a given series. The first answer is: practice, practice, practice. The second answer is that there is often more than one convergence test that can be used with a given series. I will illustrate this point…

Continuing with post on sequences and series New Series from Old 1 Rewriting using substitution New Series from Old 2 Finding series by differentiating and integrating New Series from Old 3 Rewriting rational expressions as geometric series Geometric Series – Far Out A look at doing a question the right way and the “wrong” way?…